TITLE:
Pricing Currency Call Options
AUTHORS:
Rebecca Abraham
KEYWORDS:
Laplace, Jump Process, Levy Process, Currency Calls, Weiner Process
JOURNAL NAME:
Theoretical Economics Letters,
Vol.8 No.11,
August
15,
2018
ABSTRACT: This paper presents a theoretical model to price
foreign currency call options. Currency options are employed in international
trade to reduce the risk of loss due to the reduction of revenues obtained in
depreciating foreign currency for an exporter, or the escalation of expense
from appreciating foreign currency for an importer. Other users include banks
and hedge funds who engage in currency speculation. Given the fluctuation of
option prices over time, the model describes the distribution of foreign
currency as a Weiner process for macroeconomically constrained foreign
currencies followed by a Laplace distribution for unconstrained currencies. In
a departure from existing currency option models, this model expresses foreign
currencies as dependent upon the change in macroeconomic variables, such as
inflation, interest rates, and government deficits. The distribution of
currency calls is described as a Levy process in the context of an option
trader’s risk preferences to account for the multiple discontinuities of a jump
process. The paper concludes with three models of price functions of the Weiner
process for Euro-related currency options, a Weiner process for stable currency
options, and a Levy-Khintchine process for volatile currency calls.